Decide whether you are painting only the walls or the ceiling as well. If you are going to paint the ceiling, it will be much easier to paint the walls and ceiling with the same paint. The biggest challenge in painting a two-story staircase is cutting in a straight line along the top of the walls.
Paint what you can safely reach from an upper landing. Often you can reach several feet over the staircase by standing on a stepladder at the top of the stairs.
Lean your extension ladder on the wall from the stairs. As long as there are stairs parallel to the wall, this can be done very safely and securely. If the stairs are adjacent to the wall, you will need to use a ladder leveler like the PiVit (see References.) There are several leveler designs; all provide a very solid platform for your ladder.
Do any necessary masking and repairs from the ladder. Check the bulbs in the stairwell light fixture--now is a good time to replace them.
Do all of the brush work from the ladder before rolling the walls so you don't mar freshly painted areas with the ladder. If there are areas you cannot reach otherwise, use a brush extender (also in References.) This tool attaches to your extension pole and makes it easy to paint hard-to-reach spots.
Complete any high work before painting the lower, more accessible parts of the walls. A general rule of thumb in painting is to work from the top down.